Express the sum as a common fraction: $.1 + .02 + .003 + .0004 + .00005.$
Answer: The five decimals sum to $0.12345$, which as a fraction is $\frac{12,\!345}{100,\!000}$.  Since $100,\!000=2^5\cdot 5^5$, we only have to cancel factors of 2 or 5 from $12,\!345$.  Since $12,\!345$ is odd, it has no factors of 2.  Dividing by 5, we find that $\dfrac{12,\!345}{100,\!000}=\boxed{\dfrac{2469}{20,\!000}}$.